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    GCF for 12, 18 and 60

    "Greatest Common Factor of 3 Numbers" Calculator
    Greatest Common Factor of
    ,
    and

    What's the Greatest Common Factor (GCF) of 12, 18 and 60?

    Answer

    GCF of 12, 18 and 60 is
    6

    (Six)

    6 is the largest positive integer that divides 12, 18 and 60 without a remainder — every other common divisor of the three divides it too.

    Finding the GCF of 12, 18 and 60 by Prime Factorization

    Split all three numbers into prime factors, then keep every prime that appears in all three of them, each taken as many times as it appears in the poorest factorization. Multiplying what is left gives the greatest common factor:

    All Prime Factors of 12: 2 × 2 × 3 (exponent form: 22 × 3)

    All Prime Factors of 18: 2 × 3 × 3 (exponent form: 2 × 32)

    All Prime Factors of 60: 2 × 2 × 3 × 5 (exponent form: 22 × 3 × 5)

    Prime factor121860Lowest power
    2222222
    333233
    5——5—

    GCF = 2 × 3 = 6

    Checking the GCF of 12, 18 and 60 Two Numbers at a Time

    The greatest common factor is associative, so three numbers can be handled as two pairs — and this is what makes the Euclidean algorithm usable here: run it on the first pair, then run it again on that result and the third number.

    GCF(a, b, c) = GCF(GCF(a, b), c)

    GCF(12, 18) = 6

    GCF(6, 60) = 6

    GCF(12, 18, 60) = 6

    The answer checks out by division — all three quotients come out whole:

    12 ÷ 6 = 2

    18 ÷ 6 = 3

    60 ÷ 6 = 10

    2, 3 and 10 have no common factor left — that is what makes 6 the greatest one.

    Related Calculations

    See Also

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    What is the GCF of 12, 18 and 60?. The GCF of 12, 18 and 60 is 6 — the largest number that divides all three with no remainder. Step-by-step solution for three numbers.
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    GCF Table

    Number 1Number 2Number 3GCF
    1218453
    1218462
    1218471
    1218486
    1218491
    1218502
    1218513
    1218522
    1218531
    1218546
    1218551
    1218562
    1218573
    1218582
    1218591
    1218606
    1218611
    1218622
    1218633
    1218642
    1218651
    1218666
    1218671
    1218682
    1218693
    1218702
    1218711
    1218726
    1218731
    1218742

    About "Greatest Common Factor of 3 Numbers" Calculator

    This calculator finds the Greatest Common Factor (GCF) of three numbers at once, without doing it in two passes. For example, it can help you find out what's the Greatest Common Factor (GCF) of 12, 18 and 60? (The answer is: 6). Enter the first number (e.g. '12'), the second (e.g. '18') and the third (e.g. '60'), then hit the 'Calculate' button.
    The Greatest Common Factor of three numbers — also called the greatest common divisor (GCD) or highest common factor (HCF) — is the largest positive integer that divides all three of them with zero remainder
    "Greatest Common Factor of 3 Numbers" Calculator
    Greatest Common Factor of
    ,
    and

    FAQ

    What's the Greatest Common Factor (GCF) of 12, 18 and 60?

    GCF of 12, 18 and 60 is 6

    What prime factors do 12, 18 and 60 share?

    All three factorizations contain 2 × 3, and multiplying those shared primes gives 6 — exactly the greatest common factor.

    Can you get the GCF of 12, 18 and 60 two numbers at a time?

    Yes, and it is the check this page prints. The GCF of 12 and 18 is 6, and the GCF of 6 and 60 is 6 — the same answer, because the greatest common factor is associative and does not depend on the order of the three numbers.

    How does the GCF simplify the ratio 12 : 18 : 60?

    Divide every term by the GCF 6: 12 ÷ 6 = 2, 18 ÷ 6 = 3 and 60 ÷ 6 = 10. So 12 : 18 : 60 in lowest terms is 2 : 3 : 10, and no whole number other than 1 divides all three of those.

    See Also